Observation of Quasicondensate in Two-Dimensional Atomic Hydrogen

Abstract

We have performed magnetic compression experiments with the two-dimensional gas of hydrogen atoms on liquid 4 He at T 120 200 mK. For 2D phase-space densities higher than 3, the probability of three-body dipole recombination is observed to decrease gradually by an order of magnitude in comparison to its low-density value K bbb 8.4͑3.5͒ 3 10 225 cm 4 s 21 . This is attributed to local coherence developing in a 2D quasicondensate. We have also determined the value U͞k 5.1͑5͒ 3 10 215 K cm 2 for the mean-field energy of the gas. [S0031-9007(98)07787-4] PACS numbers: 03.75.Fi, 05.30.Jp, 67.65. + z, 68.35.Rh In addition to the occupation of a single quantum state, a Bose-Einstein condensate (BEC) is characterized by long-range order or, equivalently, global coherence. The concept of quasicondensate (QC) has been introduced [1] for the lesser known situation where a boson system is coherent only locally. Having similar particle interactions, BEC and QC would be hardly distinguishable by virtue of properties related to inelastic [2,3] or elastic [4] collisions. However, the difference is transparent in spatially uniform two-dimensional (2D) system where a BEC cannot exist at finite temperature T but a QC can.In fact, a QC may appear due to interactions which suppress density fluctuations and therefore allow the 2D system to be described by a single wave function. Although the phase of the function fluctuates spatially and thus thwarts a long-range order [1], the phase coherence persists within a finite length L~exp͑sl 2 ͒ [2]. Here, l p 2ph 2 ͞mkT is the de Broglie wavelength, s is the 2D gas density, and m is the particle mass. For T ! 0 the "local BEC" regions of size L tend to extend throughout the sample and the QC turns into a "true" condensate.The appearance of a QC is to be expected when the interaction energy becomes comparable with the kinetic energy, sU ϳ kT . Here, U 4ph 2 j͞m is the mean-field parameter for elastic interactions and j is a dimensionless interaction strength. It is known that at T 0 the ratio of densities of above-condensate and condensate particles is s 0 ͞s 0 ഠ j [5]. Therefore a QC may manifest itself preferably in weakly interacting (low-j) systems.This Letter reports on the first experimental evidence for a quasicondensate in 2D atomic hydrogen gas, where we have observed a significant reduction in three-body recombination probability [2,6]. Hydrogen atoms on liquid 4 He surface occupy a single bound state with low adsorption energy, E a ͞k Ӎ 1.0 K [7]. The H adatoms are localized quite far, 8 Å, from the liquid and their out-of-plane delocalization length, l h͞ p 2E a m Ӎ 5 Å, is large compared with, e.g., the 3D scattering length a 0 0.72 Å. Thus adsorbed hydrogen may be also regarded as quasi-2D in the sense that it obeys 2D statistics while particle interactions are three dimensional [2]. It may be shown [2] that j ഠ a 0 ͞l and consequently a QC in hydrogen on 4 He may be observed at sl 2 * l͞2a 0 Ӎ 3.5.It is not easy to achieve a high degree of quantum degeneracy, i.e., high s at ...

Low-dimensional trapped gases

“…The Kosterlitz-Thouless transition has been observed in monolayers of liquid helium [14], and recently the observation of this transition has been reported for the 2D gas of spin-polarized atomic hydrogen on liquid helium surface [15]. The Kosterlitz-Thouless transition is discussed in the lectures of Benoit Douçot.…”

“…Presently, the largest obtained 2D Bose-condensed gas is the one of spin-polarized atomic hydrogen on liquid helium surface [15]. In this system the temperature is about 100 mK, the density exceeds 10 13 cm −3 , and the number of particles is ∼ 10 8 .…”

Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid

“…Other systems, such as the superconducting transition in arrays of Josephson junctions [6] and a two dimensional lattice of (3D) Bose-Einstein condensates [7], also exhibit a similar transition. Another interesting observation was in two dimensional spin polarized atomic hydrogen on liquid 4 He [8] where a reduction in three-body dipolar recombination (which is usually associated with condensation) was observed well above the BKT transition temperature. This observation results from a reduction of density fluctuations, which corresponds to quasi-condensation [9] [10].…”

Evidence of a field-induced Berezinskii–Kosterlitz–Thouless scenario in a two-dimensional spin–dimer system

“…Instead, according to the Berezinskii, Kosterlitz and Thouless (BKT) theory, a topological order may occur resulting from the binding of vortex-antivortex pairs [11][12][13] . The BKT theory has been applied to a variety of 2D phenomena in thin films, specially designed heterogeneous systems [14][15][16][17][18][19][20][21] , trapped atomic gases 22 , as well as layered bulk magnets [23][24][25][26][27][28] .…”